Embodiments herein generally relate to waveguides that are used to direct and control light. Light has two polarizations, and can propagate in a media (such as a silicon waveguide) at two different speeds for the two polarizations. For a rib/ridge waveguide, the two polarized modes are generally referred to as the transverse electric (TE) and transverse magnetic (TM) modes. The two modes may see the same media differently, as the effective refractive index for the two polarizations may differ. The difference in the effective refractive index could be the result of the symmetry of the media, or, in the case of silicon waveguides, the result of different boundary conditions for the two polarizations. The difference in the refractive index of the two polarizations can cause various adverse effects for an optical communication system and if this difference is not properly compensated for, it will cause adverse effects such as polarization mode dispersion that causes bit rate errors.
In an arrayed waveguide grating system, such as a demultiplexer, the difference in refractive index will cause the demultiplexer wavelengths to shift away from one another for the two polarizations. Such a shift will increase the crosstalk between adjacent communication channels and limit bandwidth. In particular, the difference in the refractive index for the two polarizations will cause a relative shift for the demultiplexed wavelengths:                     δλ        =                              λ            0                    ⁢                                                    n                te                            -                              n                tm                                                    n              te                                                          (        1        )            where λ0 is the center wavelength, and nte and ntm are the effective index for the TE and the TM mode, respectively.
In optical communications using wavelength division multiplexing (WDM), each wavelength channel typically uses a narrow band of wavelengths, and the separation between the channels is in the order of 1 nm. With increasing use of broadband, the channel separation could even get smaller. For λ0=1550 nm, and nte≈3.42, as typically used, a small difference in nte and ntm could result in significant performance deterioration of the system through channel cross talk. Many compensation methods have been proposed. These include the insertion of a half-wave plate in the middle of the waveguide array, dispersion matching with adjacent diffraction orders, special layer structures, insertion of a waveguide section that compensates for the polarization difference in the phase array, adding a polarization splitter at the input of the arrayed waveguide (AWG), and making a prism-shaped region at the star coupler (combiner) of the demultiplexer. While all these methods reduce or eliminate the polarization dependence, they all add significant complexity to the AWG fabrication, and for many proposed methods, they incur considerable insertion loss.
Aspects of embodiments include forming a waveguide structure on a substrate, where there is formed a base to a base height (h) above the substrate and a rectangular waveguide to a waveguide height (H) above the substrate and a waveguide width (W) between opposing sides of the waveguide. Reference, for example, a waveguide structure with the following features:H−4≦(W−3)2;  (1)H−1≧(W−4)2;  (2)H≦1.7*h+2.9; and  (3)H≧0.87*h+1.8,  (4)where:                H is the waveguide height above the substrate;        W is the waveguide width between opposing sides of the waveguide;        h is the base height above the substrate; and        * represents multiplication.        
Examples of the base height (h) are broadly from about 1 um to about 3 um above the substrate; more narrowly from about 1.5 um to about 2.5 um above the substrate; and in a specific embodiment about 2 um above the substrate. Examples of the waveguide height (H) are broadly from about 2 um to about 7 um above the substrate; more narrowly from about 3 um to about 7 um above the substrate; and in a specific embodiment about 5 um above the substrate. Examples of the waveguide width (W) are broadly from about 2 um to about 7 um; more narrowly from about 4 um to about 7 um; and in one embodiment about 6 um.
Light traveling through the waveguide comprises two polarized modes known as transverse electric (TE) and transverse magnetic (TM) modes. Producing a zero TE-TM shift was a somewhat hit or miss proposition that varies depending upon the specific requirements of each design. Using a trial and error method to vary waveguide dimensions in order to obtain near zero TE-TM shift is costly both in terms of time and resource, as each waveguide with different dimension h and H requires different etching depth or wafer thickness. Conventionally, there were no explicit rules regarding what combination of different sizes would produce a zero TE-TM shift. Indeed, as shown by the following references, which are incorporated herein by reference, conventional wisdom abandoned any type of formulation and instead required the inclusion of additional structures such as a half-wave plate in the middle of the waveguide array (H. Takashashi, Y. Hibino, and I. Nishi, Opt. Lett., Vol. 17, p. 499–501 (1992)), dispersion matching with adjacent diffraction orders (M. Zirngibl, C. H. Joyner, L. W. Stulz, T. Gaigge, and C. Dragone, Electron. Lett., Vol. 29, 201–202 (1992)), a special layer structure (H. Bissessur, F. Gaborit, B. Martin, P. Pagnod-Rossiaux, J. L. Peyre and M. Renaud, Electron. Lett., Vol. 30, p. 336–337 (1994)), insertion of a waveguide section that compensates the polarization difference in the phase array (M. Zirngibl, C. H. Joyner, and P. C. Chou, Electron. Lett., Vol. 31, p. 1662–1664 (1995)), adding a polarization splitter at the input of the AWG (M. K. Smith and C. van Dam, IEEE Journal of Selected Topics in Quantum Electronics, Vol. 5, p. 236–250 (1996)), and/or making a prism-shaped region at the star coupler (combiner) of the demultiplexer in order to consistently accomplish a zero TE-TM shift (U.S. Pat. No. 5,937,113 to He et al.). Embodiments herein go beyond simple routine experimentation and have created a methodology that will allow virtually any design to be polarization insensitive without requiring additional structures such as a half-wave plate, dispersion matching, special layers, compensating sections, a polarization splitter, prism-shaped devices, and other devices.